May 2001
Tracking Errors
| "Shallow men believe in luck. Strong men believe in cause and effect." |
| -- Ralph Waldo Emerson |
T'S BEEN ALMOST 10 MONTHS SINCE WE launched our quant portfolios. Both are attempts to track the S&P 500.
Portfolio 3 is comprised of the 30 stocks that screen the highest on our quantitative screen. It's reconstituted every 2 months. No attempt is made to balance it across sectors.
Portfolio 4 was initially sector weighted with the top screeners in each sector. Its only changes occur when there's a merger or acquisition so it's been quite stable since its inception.
In absolute terms, both portfolios have lagged the index. It doesn't take a rocket scientist to see why when you stop to consider that both have a growth tilt. After a decade of growth outperformance, the fundamental factors that screened the best were growth-oriented. Unfortunately, immediately following their creation, investors' preferences turned back to value.
Volatility
Obviously neither portfolio is closely tracking the index in absolute terms. At the very least, both are more volatile than the S&P 500. In the first few months when the index was still rising, the quant portfolios exceeded its return. The tables turned when the broad index began to fall.This is reflected in each portfolio's beta, a simple measure of relative volatility. As of mid-April, Portfolio 3 had a beta of 1.63 and Portfolio 4 had a beta of 1.22.
What does this tell us? In general, a well-diversified portfolio's beta will tell you how it will react relative to the appropriate index. For
example, if a portfolio has a beta of 1.1 and the index rises 10%, it will rise 11% (1.1 x 10%). If the index falls by 20%, the portfolio will decline 22% (1.1 x -20%).
We can apply this analysis over the first nine months of our quant portfolios' existence. From June 30, 2000 to April 6, 2001, the S&P 500 fell 22.42%. Applying the portfolios' betas yields an expected return of -36.54% for Portfolio 3 and -27.35% for Portfolio 4. In both instances, actual losses far exceeded the predictions (63.84% and 35.72%, respectively).
You can draw several conclusions from these results. First, recall beta is a good measure of volatility for a well diversified portfolio. Portfolio 3 certainly isn't exceptionally diversified and although Portfolio 4 has holdings in each S&P 500 sector, it still lacks the diversification of the broad index. In this instance, standard deviation, not beta, may be a better measure of volatility.
Secondly, we can only consider data from the past nine months. That's a pretty short period of time to base conclusions based on long-term measures of volatility. Perhaps it's just too soon to arrive at any definitive conclusion.
|
| |||||
|
Nevertheless, we suspect the excess volatility in our portfolios indicates that the fundamental factors in our quantitative models fall short of explaining the variability of returns. In other words, our models don't fully capture the factors that determine performance. There's another way to test this.
Correlation
Think back to 7th grade algebra. If you have two series of numbers, you can graph them together to see how they move relative to one another. By using a little math, you can get the best-fit line to explain their relation.If the two series move identically, it's a perfect positive correlation. If one moves up when the other moves down, they're negatively correlated. If there's no distinguishable relation between the series' movements, they aren't correlated and have a correlation coefficient near 0.
The daily changes in Portfolio 3, Portfolio 4, and the S&P 500 are series that can be tested for correlation. If our models are really doing their job, the portfolios should be highly correlated with the index.
Bearing in mind we still have only nine months of data, we ran the regressions to get the coefficients of correlation for each portfolio and the S&P 500. The accompanying charts show the resulting regression equation.
As we suspected, the correlations -- while respectable -- aren't especially high: .7552 for Portfolio 3 and .8483 for Portfolio 4. As you would expect by its higher correlation coefficient, Portfolio 4 is much closer to the index than Portfolio 3. Looking at the graphs this makes sense since the points for Portfolio 4 vs. the S&P 500 are bunched closer together than those for Portfolio 3.
|
|
 This graph compares the daily returns of Portfolio 3 to those of the S&P 500. They're dispersed about the red regression line, indicating the two are not highly correlated.
|
If you can stand a little more math, the square of the correlation coefficient is the coefficient of determination known as the R2. It represents the amount of variation explained by the regression model.
For Portfolio 3, the R2 is only .5704 while Portfolio 4 is a little better with at .7195. In other words, movements in Portfolio 4 explain just a little over half of the movement in the S&P 500. Portfolio 4 is a little better, explaining about 75% of the index's change. To make matters worse, neither of these is statistically meaningful at the 95% level of significance.
So What Does it Mean?
That's a lot of statistical mumbo-jumbo, but none of it is too encouraging. In plain English, if our models were really doing what we want them to do, they'd be highly correlated with the S&P. Instead, correlations are mediocre and variation relative to the index is high.This looks worse in today's down market than it would with a raging bull. Presumably in an up market, the portfolios would outperform by similar amounts.
Regardless of which way the models miss, the problem is tracking error, the difference between the portfolio return and that of the S&P 500. The models were designed to track the index and so far they don't appear to be doing that.
Of course it is still early, with only nine months worth of data. We'll keep an eye on it, but at this point the statistics aren't particularly encouraging. That's why this is still a work in progress.
Search this site! Just enter you key word or words:
Get current quotes or follow your own custom portfolio,
courtesy of E-Line Financials:
|
|||||||||||
| Homepage | Return to Top |
